Stochastic Stability of Differential Equations in Abstract Spaces
London Mathematical Society Lecture Note Series

The stability of stochastic differential equations in abstract, mainly Hilbert, spaces receives a unified treatment in this self-contained book. It covers basic theory as well as computational techniques for handling the stochastic stability of systems from mathematical, physical and biological problems. Its core material is divided into three parts devoted respectively to the stochastic stability of linear systems, non-linear systems, and time-delay systems. The focus is on stability of stochastic dynamical processes affected by white noise, which are described by partial differential equations such as the Navier?Stokes equations. A range of mathematicians and scientists, including those involved in numerical computation, will find this book useful. It is also ideal for engineers working on stochastic systems and their control, and researchers in mathematical physics or biology.

Preface; 1. Preliminaries; 2. Stability of linear stochastic differential equations; 3. Stability of non linear stochastic differential equations; 4. Stability of stochastic functional differential equations; 5. Some applications related to stochastic stability; Appendix; References; Index.

Kai Liu is a mathematician at the University of Liverpool. His research interests include stochastic analysis, both deterministic and stochastic partial differential equations, and stochastic control. His recent research activities focus on stochastic functional differential equations in abstract spaces. He is a member of the editorial boards of several international journals including the Journal of Stochastic Analysis and Applications and Statistics and Probability Letters.